scholarly journals A Generalized Finite Volume Method for Density Driven Flows in Porous Media

Energies ◽  
2021 ◽  
Vol 14 (19) ◽  
pp. 6151
Author(s):  
Yueyuan Gao ◽  
Danielle Hilhorst ◽  
Huy Cuong Vu Do
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Space Dimension ◽  
Salt Water ◽  
Test Case ◽  
Adaptive Meshes ◽  
Dimension 2 ◽  
Numerical Discretization ◽  
Volume Method ◽  
Time Evolution Equation

In this article, we consider a time evolution equation for solute transport, coupled with a pressure equation in space dimension 2. For the numerical discretization, we combine the generalized finite volume method SUSHI on adaptive meshes with a time semi-implicit scheme. In the first part of this article, we present numerical simulations for two problems: a rotating interface between fresh and salt water and a well-known test case proposed by Henry. In the second part, we also introduce heat transfer and perform simulations for a system from the documentation of the software SEAWAT.

Application of Finite Volume Method for Solid Mechanics

2003 ◽  
Author(s):  
Bryce L. Fowler ◽  
Raymond K. Yee
Keyword(s):  
Finite Element ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Solid Mechanics ◽  
Preliminary Test ◽  
Test Case ◽  
Element Analysis ◽  
Vibration Isolators ◽  
Incompressible Materials ◽  
Volume Method

Polymers constitute a large class of nearly incompressible solid materials (i.e., Poisson’s Ratio near 0.5). These materials are often used as passive vibration isolators. Accurately modeling vibration isolators made of nearly incompressible materials has been extremely difficult with standard finite element analysis. This paper provides an alternative to the specialized finite element formulations currently used to model incompressible materials. The finite volume methodology of computational fluid dynamics is employed in this paper to solve the Hooke’s Law equations in solid mechanics. Test cases have been performed to evaluate the performance of finite volume method applied to solid mechanics problems. The formulation has been coded in Matlab for practical use. Based on the preliminary test case results, the finite volume formulation compares favorably to finite element method.

scholarly journals Observation of vector solitary waves in soft laminates using a finite volume method

2020 ◽  
Author(s):  
Ron Ziv ◽  
Gal Shmuel
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Solitary Waves ◽  
Nonlinear Waves ◽  
Space Dimension ◽  
Soft Materials ◽  
Circularly Polarized ◽  
Higher Dimensional ◽  
Linearly Polarized ◽  
Volume Method

Soft materials with engineered microstructure support nonlinear waves which can be harnessed for various applications, from signal communication to impact mitigation. Such waves are governed by nonlinear coupled differential equations whose analytical solution is seldom trackable, hence emerges the need for suitable numerical solvers. Based on a finite-volume method in one space dimension, we here develop a designated scheme for nonlinear waves with two coupled components that propagate in soft laminates. We apply our scheme to a periodic laminate made of two alternating compressible Gent layers, and consider two cases. In one case, we analyze a motion whose component along the lamination direction is coupled to a component in the layers plane, and discover vector solitary waves in a continuum medium. In the second case, we analyze a motion with two coupled components in the plane of the layers, and observe a train of linearly polarized solitary waves, followed by a single circularly polarized wave. The framework we developed offers a platform for further investigation of these waves and their extension to higher dimensional problems.

scholarly journals Postprocessing of standard finite element velocity fields for accurate particle tracking applied to groundwater flow

2020 ◽  
Vol 24 (4) ◽  
pp. 1605-1624
Author(s):  
Philipp Selzer ◽  
Olaf A. Cirpka
Keyword(s):  
Finite Element ◽  
Velocity Field ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Particle Tracking ◽  
Mass Conservation ◽  
Velocity Fields ◽  
Test Case ◽  
Hydraulic Gradients ◽  
Volume Method

Abstract Particle tracking is a computationally advantageous and fast scheme to determine travel times and trajectories in subsurface hydrology. Accurate particle tracking requires element-wise mass-conservative, conforming velocity fields. This condition is not fulfilled by the standard linear Galerkin finite element method (FEM). We present a projection, which maps a non-conforming, element-wise given velocity field, computed on triangles and tetrahedra, onto a conforming velocity field in lowest-order Raviart-Thomas-Nédélec ($\mathcal {RTN}_{0}$ R T N 0 ) space, which meets the requirements of accurate particle tracking. The projection is based on minimizing the difference in the hydraulic gradients at the element centroids between the standard FEM solution and the hydraulic gradients consistent with the $\mathcal {RTN}_{0}$ R T N 0 velocity field imposing element-wise mass conservation. Using the conforming velocity field in $\mathcal {RTN}_{0}$ R T N 0 space on triangles and tetrahedra, we present semi-analytical particle tracking methods for divergent and non-divergent flow. We compare the results with those obtained by a cell-centered finite volume method defined for the same elements, and a test case considering hydraulic anisotropy to an analytical solution. The velocity fields and associated particle trajectories based on the projection of the standard FEM solution are comparable to those resulting from the finite volume method, but the projected fields are smoother within zones of piecewise uniform hydraulic conductivity. While the $\mathcal {RTN}_{0}$ R T N 0 -projected standard FEM solution is thus more accurate, the computational costs of the cell-centered finite volume approach are considerably smaller.

Simulation of Rotor/Stator Interaction With a 4D Finite Volume Method

2002 ◽  
Author(s):  
Bjo¨rn Laumert ◽  
Hans Ma˚rtensson ◽  
Torsten H. Fransson
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Three Dimensional ◽  
Test Case ◽  
Pressure Distributions ◽  
Time Space ◽  
Rotor Stator Interaction ◽  
Pitch Ratio ◽  
Grid Nodes ◽  
Volume Method

A finite volume method for the computation of rotor/stator interaction for stages with arbitrary rotor/stator pitch ratios is presented and partly validated in this paper. The method which solves the unsteady three-dimensional Euler equations is formulated in the four-dimensional time-space domain. The method of time inclination is utilized to account for unequal pitchwise periodicity by distributing time co-ordinates at the grid nodes such that phase lagged boundary conditions can be employed. Calculated results show excellent agreement with the results of a reference solver for the validation test case. Furthermore the method was applied to the simulation of the unsteady flow field in a transonic test turbine stage with a stator/rotor pitch ratio of 1.875. The results were compared with measurements of the unsteady rotor blade pressure and a reference solver calculation where an approximate pitch ratio of 2.0 with a 6.7% scaled rotor geometry was employed. Both computational cases show satisfactory agreement with the experiments for both time averaged pressure distributions and pressure perturbation amplitudes.

A comparison of finite volume method and sharp model for two dimensional saltwater intrusion modeling

2014 ◽  
Vol 41 (3) ◽  
pp. 191-196 ◽  
Author(s):  
Boutaina Bouzouf ◽  
Zhi Chen
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Saltwater Intrusion ◽  
Mathematical Formulation ◽  
Test Case ◽  
Two Phase ◽  
Closed Form Solutions ◽  
Analytical Test ◽  
Mathematical Equations ◽  
Volume Method

Seawater intrusion in coastal aquifers is a 3-D phenomenon. However, 3-D regional aquifer models are often limited by insufficient geological and hydrological data, the large horizontal to vertical scales ratio, and by numerical constraints. A mathematical formulation and numerical implementation of the model for saltwater intrusion problems are presented in this paper. The mathematical model is based on assumption of two-phase flow between saltwater and freshwater and Dupuit approximation. Finite volume method is used as the numerical method in non-structured grids to have flexibility upon complex configuration domain and was compared to sharp model that uses finite difference method. Both models are based on the same governing mathematical equations. Finite volume method was validated using analytical test case studies with known closed form solutions, and the results showed good agreement. Both models have then been applied to the case of saltwater intrusion into a real study case. The comparison between both methods indicates that the finite volume method provides predictions closer to the observed results.

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